Answer:2000
Step-by-step explanation:2500x0.2=500
2500-500=2000
Answer:
the dimensions of the box that minimizes the cost are 5 in x 40 in x 40 in
Step-by-step explanation:
since the box has a volume V
V= x*y*z = b=8000 in³
since y=z (square face)
V= x*y² = b=8000 in³
and the cost function is
cost = cost of the square faces * area of square faces + cost of top and bottom * top and bottom areas + cost of the rectangular sides * area of the rectangular sides
C = a* 2*y² + a* 2*x*y + 15*a* 2*x*y = 2*a* y² + 32*a*x*y
to find the optimum we can use Lagrange multipliers , then we have 3 simultaneous equations:
x*y*z = b
Cx - λ*Vx = 0 → 32*a*y - λ*y² = 0 → y*( 32*a-λ*y) = 0 → y=32*a/λ
Cy - λ*Vy = 0 → (4*a*y + 32*a*x) - λ*2*x*y = 0
4*a*32/λ + 32*a*x - λ*2*x*32*a/λ = 0
128*a² /λ + 32*a*x - 64*a*x = 0
32*a*x = 128*a² /λ
x = 4*a/λ
x*y² = b
4*a/λ * (32*a/λ)² = b
(a/λ)³ *4096 = 8000 m³
(a/λ) = ∛ ( 8000 m³/4096 ) = 5/4 in
then
x = 4*a/λ = 4*5/4 in = 5 in
y=32*a/λ = 32*5/4 in = 40 in
then the box has dimensions 5 in x 40 in x 40 in
Answer:
B
Step-by-step explanation:
On a coordinate plane, an exponential function increases in
quadrant 3 into quadrant 4 and approaches y = 0. It goes through
(negative 1, negative 2) and crosses the y-axis at (0, negative 0.25) ⇒ last answer
HOPE IT HELPS ....
Answer:
The number of kids NOT wearing socks in the gym = 20
Step-by-step explanation:
Here, the total number of kids in the gym = 80
Now, 75% of the kids are wearing socks.
Let us assume the number of kids wearing socks = m
⇒ 75 % of 80 = m
Calculating the value of m ,we get:
⇒ 60 kids are wearing socks.
Kids not wearing socks = Total kids in gym - Kids wearing socks
= 80 - 60 = 20
Hence, the number of kids NOT wearing socks in the gym = 60.
